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Zbl 0632.18001
Ehrbar, Hans; Wyler, Oswald
Images in categories as reflections. (English)
[J] Cah. Topologie Géom. Différ. Catég. 28, No. 1-2, 143-159 (1987). ISSN 1245-530X

The paper under review is based on joint work by the two authors, carried out in 1968/69 and not published until now (except for a preliminary technical report). As in the past, the image of a morphism $f: A\to B$ of a category C is defined with respect to a subclass M of C via a factorization with a certain ``global'' diagonal property. This property is equivalent to the existence of a reflection for M in the category of commutative squares of C. \par Although the generality of the presentation (which includes discussions of the dual concepts) may be of some interest to old-time categorists, the dependence of the notion of image on a choice of the subclass M renders the application of the results more troublesome than beneficial. Indeed, in most concrete categories the image of f is (or should be) the kernel of the pair of insertions $B\rightrightarrows\sp{u}\sb{v}S$ associated with the amalgamated sum S of $B\leftarrow\sp{f}A\to\sp{f}B$.
[J.Sonner]

MSC 2000:: *18A32 Factorization of morphisms
18A40 Adjoint functors
18A20 Special classes of morphisms

Keywords: images; coimages; factorization of morphisms; reflective subcategories

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